26 April 2004 1
A Compositional Framework for Real-Time Guarantees
Insik Shin and Insup Lee
Real-time Systems GroupSystems Design Research Lab
Dept. of Computer and Information Science
University of Pennsylvania
26 April 2004 2
SDRL & RTGDepart. Of Computer and
Information Science
Scheduling Framework Example
CPU
OS Scheduler
Digital Controller Multimedia
Periodic Task T(p,e)
T1(25, 5)
Periodic Task T(p,e)
T2(33, 10)
26 April 2004 3
SDRL & RTGDepart. Of Computer and
Information Science
Motivating Example
CPU
OS Scheduler
Java Virtual Machine
J1(25,4) J2(40,5)
VM Scheduler
Multimedia
T2(33,10)
Digital Controller
T1(25,5)
26 April 2004 4
SDRL & RTGDepart. Of Computer and
Information Science
VM Scheduler’s Viewpoint
CPU
OS Scheduler
Multimedia
T2(33,10)
Digital Controller
T1(25,5)
Java Virtual Machine
J1(25,4) J2(40,5)
VM Scheduler
CPU Share
Real-Time Guarantee on CPU Supply
26 April 2004 5
SDRL & RTGDepart. Of Computer and
Information Science
Problems & Approach I
• Resource supply modeling– Characterize temporal property of resource
allocations
• we propose a periodic resource model
– Analyze schedulabilitywith the new resource model
Java Virtual Machine
J1(25,4) J2(40,5)
VM Scheduler
Periodic CPU Share
26 April 2004 6
SDRL & RTGDepart. Of Computer and
Information Science
OS Scheduler’s Viewpoint
CPU
OS Scheduler
Java Virtual Machine
J1(25,4) J2(40,5)
VM Scheduler
Multimedia
T2(33,10)
Digital Controller
T1(25,5) Real-Time Task
Real-Time Demand
26 April 2004 7
SDRL & RTGDepart. Of Computer and
Information Science
Problem II
• Real-Time Composition– Combine multiple real-time requirements into a
single real-time requirement guaranteeing schedulability
– Example: periodic task model T(p,e)
Real-Time Constraint
Real-Time Constraint
Real-Time Constraint
EDF/RM
T1 (3, 1) T2 (4, 1) T (?, ?)
26 April 2004 8
SDRL & RTGDepart. Of Computer and
Information Science
Approach II
• Simple approach : T(p,e)– p = LCM (T1, T2) LCM (T1, T2) = T1xN1 =
T2xN2
– e = p x (U1+ U2), Ui= ei/pi
EDF
T1 (3, 1) T2 (4, 1) T (12, 7)T (?, ?)
(12,7)T
5 10 15120 3
Deadline Miss !
26 April 2004 9
SDRL & RTGDepart. Of Computer and
Information Science
Approach II
• Our approach : periodic task model T(p,e)
EDF
T1 (3, 1) T2 (4, 1) T (2, 4/3)
(12,7)T
5 10 15120 3
(12,7)T
10 15120 32 4 6 8
26 April 2004 10
SDRL & RTGDepart. Of Computer and
Information Science
Outline
1. Scheduling component modeling• Periodic resource model
2. Scheduling component schedulability analysis3. Scheduling component composition
• Combine the real-time guarantees of multiple components into the real-time guarantee of a single component
26 April 2004 11
SDRL & RTGDepart. Of Computer and
Information Science
Scheduling Component Modeling
• Scheduling– assigns resources to workloads by algorithms
• Scheduling Component Model : M(W,R,A)– W : workload model– R : resource model– A : scheduling algorithm
Resource
Scheduler
WorkloadPeriodic Task WorkloadPeriodic Task
EDF / RM
???
26 April 2004 12
SDRL & RTGDepart. Of Computer and
Information Science
Resource Modeling
• Dedicated resource– Available all the time at its full capacity
0 time
26 April 2004 13
SDRL & RTGDepart. Of Computer and
Information Science
Resource Modeling
• Dedicated resource– Available all the time at its full capacity
• Fractional resource (slow resource) – Available all the time at its fractional capacity
0 time
26 April 2004 14
SDRL & RTGDepart. Of Computer and
Information Science
Resource Modeling
• Dedicated resource– Available all the time at its full capacity
• Fractional resource (slow resource)– Available all the time at its fractional capacity
• Partitioned resource [FeMo ’02]– Available all some times at its full capacity
0 time
26 April 2004 15
SDRL & RTGDepart. Of Computer and
Information Science
Resource Modeling
• Dedicated resource– Available all the time at its full capacity
• Fractional resource (slow resource)– Available all the time at its fractional capacity
• Partitioned resource– Available all some times at its full capacity
• Periodic resource R(period, allocation time) (ex. R(3,2))
– Available periodically at its full capacity
0 time
26 April 2004 16
SDRL & RTGDepart. Of Computer and
Information Science
T2(20,4)T1(10,2)
Scheduling Component Analysis
• Schedulability conditions– Exact conditions for EDF/RM
• Schedulability bounds– Utilization bounds for periodic workload under
EDF/RM– Capacity bounds for periodic resource under
EDF/RM
Periodic Resource
Scheduler
Periodic Task Periodic Task
EDF / RM
26 April 2004 17
SDRL & RTGDepart. Of Computer and
Information Science
Schedulability Conditions (EDF)
• Scheduling component M(W,R,EDF) is schedulable iff for all interval length t, demandw(EDF,t) ≤ supplyR(t) [RTSS03]
– demandw(EDF,t) : the maximum resource demand of workload W for an interval length t
– supplyR(t) : the minimum resource supply by resource R for an interval length t
i
ni ie
p
t
1
demand(EDF,t) =
26 April 2004 18
SDRL & RTGDepart. Of Computer and
Information Science
• supply =
• supply =
• supplyR(3) = 1
0 time
0 time
3
1
R(3,2)
R(3,2)
t
26 April 2004 19
SDRL & RTGDepart. Of Computer and
Information Science
Schedulability Conditions (RM)
• Scheduling component M(W,R,RM) is schedulable iff
for all task Ti(pi,ei),
ri(R) ≤ pi [RTSS03]
– ri(R): the maximum response time of task Ti
over R. the smallest time t s.t.
demand(RM,i,t) ≤ supplyR(t) k
THPT ki e
p
te
ik
)(
demand(RM,i,t) =
26 April 2004 20
SDRL & RTGDepart. Of Computer and
Information Science
Schedulability Conditions (RM)
• Scheduling component M(W,R,RM) is schedulable iff for all task Ti(pi,ei),
ri(R) ≤ pi [RTSS03]
– Example of finding the maximum response time ri(R)
time
resource demand
ri(R)
demand(RM,i,t)
supplyR(t)
26 April 2004 21
SDRL & RTGDepart. Of Computer and
Information Science
Motivating Example for Capacity Bound
• Given a task group G such that – Scheduling algorithm : EDF
– A set of periodic tasks : { T1(3,1), T2(7,1) },
model the timing requirements of the task group with a periodic task model
• G (3, 1.43) based on utilization does not work !!
10 432 65 987
Deadline miss for T2
26 April 2004 22
SDRL & RTGDepart. Of Computer and
Information Science
Motivating Example (2)
• Given a task group G such that – Scheduling algorithm : EDF
– A set of periodic tasks : { T1(3,1), T2(7,1) },
model the timing requirements of the task group with a periodic task model
• G (3, 2.01) works !!
10 432 65 987
26 April 2004 23
SDRL & RTGDepart. Of Computer and
Information Science
Capacity Bounds
• Resource capacity– For a periodic resource R(p,e), its capacity is e/p.
• Capacity bound of a component C(W, R(p,e), A) : CB(C)– C is schedulable if CB(C) ≤ e/p
• How to get the capacity bounds of C(W,R(p,e),A)
– assumption: the period p of R is given. – using the exact schedulability conditions, we can
get the minimum capacity of R satisfying the condition.
T1(25,4)
T2(40,5)EDF
R(10, ? )R(10, 3.1)CB(C) = 3.1/10
26 April 2004 24
SDRL & RTGDepart. Of Computer and
Information Science
Compositional Real-Time Guarantees
T11(25,4)
T12(40,5)
T21(25,4)
T22(40,5)
R(?, ?)
EDF
EDF RM
R2(?, ?)R1(?, ?)R1(10, 3.1) R2(10, 4.34)
26 April 2004 25
SDRL & RTGDepart. Of Computer and
Information Science
Compositional Real-Time Guarantees
T21(25,4)
T22(40,5)
R(?, ?)
EDF
RM
R(5, 4.4)
R2(10, 4.4)
T2(10, 4.4)
T11(25,4)
T12(40,5)EDF
R1(10, 3.1)
T1(10, 3.1)
26 April 2004 26
Conclusion
• Summary– Periodic resource model– Scheduling component modeling and anaylsis– Scheduling component composition
• Future work– To evaluate the composition overhead in current
framework– To extend our framework with other resource models for
• Efficient composition w.r.t utilization and complexity• Ensure composition properties, i.e.,
– C1 || (C2 || C3) = (C1 || C2 ) || C3
– || (C1, C2, C3) = || (||(C1, C2), C3)
26 April 2004 27
SDRL & RTGDepart. Of Computer and
Information Science
THE
THE END
END
ENDTHE
THANK YOU
26 April 2004 28
SDRL & RTGDepart. Of Computer and
Information Science
Schedulability Conditions (EDF)
• Scheduling component M(W,R,EDF) is schedulable iff for all interval length t,
demandw(t) ≤ t [BHR90]
demandw(t) ≤ supplyR(t)
– demandw(t) : the maximum resource demand of
workload W over all intervals of length t
– supplyR(t) : the minimum resource supply by resource R over all intervals of length t
Resource demand in an interval
Resource supply during the interval
(from a dedicated resource)
26 April 2004 29
SDRL & RTGDepart. Of Computer and
Information Science
• Scheduling component M(W,R,RM) is schedulable iff for all task Ti(pi,ei),
ri ≤ pi [AB+93]
durationR(ri) ≤ pi
– ri : the maximum response time of task Ti
: the maximum resource demand of W to finish Ti
– durationR(t) : the maximum time that resource R takes to supply a t-time-unit resource
Schedulability Conditions (RM)
Duration to receive ri-time-unit
resource allocation
Deadlineto receive ri-time-unit
resource allocation
Max. Duration to receive ri-time-unit
resource allocation
Deadlineto receive ri-time-unit
resource allocation